Question: $\vec u = (-6,-9)$ $\vec w = (5, -4)$ $\dfrac13\vec u + \dfrac12\vec w= (~ $
Solution: Strategy overview This question asks us to perform the following: Scalar multiplication Vector addition Solution steps $\begin{aligned} {\dfrac13}\vec u + {\dfrac12}\vec w &= {\dfrac13}(-6,-9) + {\dfrac12}(5,-4) \\\\\\\\ &= (-2, -3) + (2.5, -2) \\\\\\\\ &= (-2+ 2.5, -3+ (-2)) \\\\ &= (0.5, -5) \\\\ \end{aligned}$ The answer $( 0.5, -5 )$